Alan Turing and the foundations of computable analysis
We investigate Turing's contributions to computability theory for real numbers and real functions presented in [22, 24, 26]. In particular, it is shown how two fundamental approaches to computable analysis, the so-called ‘Type-2 Theory of Effectivity' (TTE) and the ‘realRAM machine' model, have their foundations in Turing's work, in spite of the two incompatible notions of computability they involve. It is also shown, by contrast, how the modern conceptual tools provided by these two paradigms allow a systematic interpretation of Turing's pioneering work in the subject.
Permanent link to this document: http://projecteuclid.org/euclid.bsl/1309952319
Digital Object Identifier: doi:10.2178/bsl/1309952319
Zentralblatt MATH identifier: 05956504
Mathematical Reviews number (MathSciNet): MR2856079